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Full text of "Analytical Mechanics"

MOTION OF A PARTICLE
119
108. E. Atwood's Machine.  The problem is to find the equations of motion of two particles connected by means of a string of negligible mass which is slung over a smooth pulley.
Let mi and m2 be the masses of the particles. Then considering each particle separately we obtain the following for the force equations:

-at
(a) (b)
where T is the tensile force in the string. Eliminating T between equations (a) and (b) we obtain
dv (mi + m*)  = (mi - w2) g,        (c)
dt dv dt
(d)
FIG. 65.
Therefore the acceleration is constant and consequently the equations of motion are obtained by substituting this value of the acceleration in equations (1) to (3) of page 113:
s =
 m<2,
dv
Eliminating -7- between equations (a) and (b) we have
(e)